Categorical Data Analysis Review of Part I Categorical Data Analysis Some Basic Concepts: 1. Types of Variables Binary Variable Nominal Variable Ordinal Variable Discrete Variable Continuous Variable Categorical Variable 1/16/2019 SA3202, Review of Part I

2. Categorical Data Contingency Table One-Way Table Two –Way Table 3. The Pearson’s Goodness of Fit Test and The Wilk’s Likelihood Ratio Test 1/16/2019 SA3202, Review of Part I

The Probability Models Discrete The Equi-probability Model The Binomial Distribution Model The Multinomial Distribution Model The Poisson Distribution Model Others Continuous The Uniform Distribution The Normal Distribution 1/16/2019 SA3202, Review of Part I

The Binomial Distribution Bernoulli Variable Binomial Variable Estimation Asymptotic Normality CI Hypothesis Testing 1/16/2019 SA3202, Review of Part I

III The Multinomial Distribution Multinomial Trial Multinomial R.V. Marginal Distribution Estimation CI Hypothesis Testing 1/16/2019 SA3202, Review of Part I

IV Test Composite Hypotheses Case I. The hypothesis imposes restrictions on the possible values of the parameters df=k-# of independent restrictions Case II. The hypothesis assume a model for the probabilities in terms of a small number of parameters Df=k-1-# of free parameters estimated under H0 1/16/2019 SA3202, Review of Part I

V. Goodness of Fit Test Procedure: Step1 Transform the data into categorical data via range divisions Step2 Apply the Pearson’s Goodness of fit test or Wilk’s Likelihood ratio test For Discrete Distributions For Continuous Distributions 1/16/2019 SA3202, Review of Part I

VI. Independence Test for 2x2 Table Response Group 1 Group 2 Positive X1 X2 Negative n1-X1 n2-X2 Total n1 n2 Distribution Estimation CI Hypothesis Testing 1/16/2019 SA3202, Review of Part I

VII. Association Measures for 2x2 Tables Proportion Difference Odds Ratio Log Odds Ratio 1/16/2019 SA3202, Review of Part I

VIII. Independence Test for 2xk Table Response Group 1 Group 2 ….. Group k Total Positive X1 X2 …… Xk Negative n1-X1 n2-X2 …… nk-Xk Total n1 n2 nk H0: The pooled sample proportion The Estimated Expected Frequency The Test Statistic 1/16/2019 SA3202, Review of Part I

IX. Probability Structure for rxc Table Response 1 2 3….. c Total 1 p11 p12 p13 p1c 2 p21 p22 p23 p2c ………………………………………………… r pr1 pr2 pr3 prc Total The Joint Distribution The Marginal Distribution The Conditional Distribution 1/16/2019 SA3202, Review of Part I

X. Independence Test for rxc Table Response 1 2 3….. c Total 1 X11 X12 X13….. X1c 2 X21 X22 X23……. X2c ………………………………………………… r Xr1 Xr2 Xr3 Xrc Total H0: The Estimated Expected Frequency The Test Statistic 1/16/2019 SA3202, Review of Part I

XI. Sampling Procedures for rxc Table 1. Simple Random Sampling Response 1 2 3….. c Total 1 X11 X12 X13….. X1c 2 X21 X22 X23……. X2c ………………………………………………… r Xr1 Xr2 Xr3 Xrc Total n 1/16/2019 SA3202, Review of Part I

Stratified Random Sampling with C Response 1 2 3….. c Total 1 X11 X12 X13….. X1c 2 X21 X22 X23……. X2c ………………………………………………… r Xr1 Xr2 Xr3 Xrc Total n1 n2 n3 nc n 1/16/2019 SA3202, Review of Part I

3. Stratified Random Sampling with R Response 1 2 3….. c Total 1 X11 X12 X13….. X1c m1 2 X21 X22 X23……. X2c m2 ………………………………………………… r Xr1 Xr2 Xr3 Xrc mr Total n 1/16/2019 SA3202, Review of Part I